An asymptotic behavior of the dilatation for a family of pseudo-Anosov braids

Kodai Mathematical Journal

Mitsuhiko Takasawa¹  Eiko Kin¹ 

[1] Department of Mathematical and Computing Sciences Tokyo Institute of Technology

关键词: mapping class group;    braid;    pseudo-Anosov;    dilatation;   

DOI  :  10.2996/kmj/1206454554

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(10)The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids with arbitrarily small dilatation such that the mapping torus obtained from such braid has 2 cusps and has an arbitrarily large volume.

【 授权许可】

Unknown